MEASUREMENT OF DISCHARGE BY PRECALIBRATED MEASURING STRUCTURES
7.8 TRANSFERABILITY OF LABORATORY RATINGS
The transfer of a laboratory discharge rating to a structure in the field requires the existence, and maintenance, of similitude between laboratory model and prototype, not only with regard to the structure, but also with regard to the approach channel. For example, scour and/or fill in the approach channel will change the head-discharge relation, as will algae growth on the control structure.
Both the structure and the approach channel must be kept free from accumulation of debris, sediment, and vegetal growth. Flow conditions downstream from the structure are significant only to the extent that they control the tailwater elevation, which may influence the operation of structures designed for free-flow conditions.
However there are now some 800 measuring structures in operation in the United Kingdom in the national network. These structures, some of which are compound (see Figure I.7.15) have generally been installed where the velocity area method was unsuitable. Many of them operate in the non-modular range by means of a crest tapping.
See Herschy et al., (1977) and ISO 4360 (2005).
Crest tapping is an array of holes along the crest of the weir. These tapping holes (usually 5 to 10 holes Figure I.7.13. River Grwyne at Millbrook:
South Wales. Single crest crump weir
of 10 mm diameter) are connected through an arrangement of tubes and a manifold to transmit the static head along the crest to the gauge. Check calibrations have been carried out over the years and it has been found that no significant departure from the laboratory rating has occurred (White 1975). The critical factor in all measuring structures is the accurate measurement of head. Any change in the coefficient of discharge is usually negligible compared to the uncertainty in measuring head.
7.9 ACCURACY
The following discussion on accuracy and uncertainty for weirs and flumes relate directly to equations and tables in the preceding discussion.
For additional information on determination of uncertainty see Chapter 10 of this Manual.
The basic error equation for the estimation of the uncertainty in a single determination of discharge for a weir is as follows:
Figure I.7.14. River Ellen at Bullgill. North West England: Flat-v low flow control weir.
Figure I.7.15. River Colne at Berrygrove. South East England. Compound crump weir.
if Q = Cbhn
then XQ (
(
Xc2Xb2n X2 h2 1/2)
(7.17)where C = coefficient of discharge; b = length of crest; h = gauged head; n = exponent of h, usually 3/2 for a weir and 5/2 for a V-notch; XQ = percentage uncertainty in a single determination of discharge;
Xc = percentage random uncertainty in the value of the coefficient of discharge; Xb = percentage random uncertainty in the measurement of the length of crest; Xh = percentage random uncertainty in the measurement of gauged head.
All values of uncertainties are standard deviations at the 95 per cent level. The percentage uncertainty will vary with discharge and should be computed for a range of expected stage values.
7.9.1 Thin-plate weirs
The value of n in equation 7.17 is taken as 1.5 for rectangular thin-plate weirs and 2.5 for V-notches and the uncertainty in the coefficient Xc may be taken as ± 1.0 (ISO 1438, 2005).
7.9.2 Triangular profile (Crump) weirs The random uncertainty Xc, in percent, is given by the following equation:
Xc ((10Cv<9) (7.18)
Values of Cv for the purpose of this equation are given in Table I.7.4. However, for normal field installations Xc can generally be taken as ± 2 per cent.
7.9.3 Round-nosed horizontal crest weirs
The random uncertainty, Xc, in percent, in the value of the coefficient is:
Xc (2(21 - 20CD) (7.19) where CD is computed by equation 7.11.
7.9.4 Rectangular profile weirs
The random uncertainty Xc, in percent, in the value of the coefficient is:
Xc ((10F<8 ) (7.20)
where F is the coefficient correction factor. Values of F for given values of h/L and h/(h + P) are obtained from Table I.7.5.
7.9.5 Standing wave flumes
For a flume, the error equation may be expressed as follows:
XC (Xc2A X2 b2B X2 h2C X2 s2 1/2) (7.21) where XQ = random uncertainty in a single determination of discharge; Xc = random uncertainty in the value of the coefficient; Xb = random uncertainty in the width of throat; Xh = random uncertainty in the measurement of gauged head; Xs = random uncertainty in the slope at the throat; A, B, C = numerical coefficients depending on the flume geometry, for example for a rectangular flume A = 1, B = 1.5 and C = 0 and for a U-shaped flume C = 0.
Values of A, B and C can be obtained from Table I.7.11 for trapezoidal and U-shaped flumes.
Table I.7.11. Values of numerical coefficients for trapezoidal and U-shaped flumes
Trapezoidal flumes U-shaped flumes
mh/b A B C h/D A B
0.01 0.99 1.51 0.01 – – –
0.03 0.97 1.53 0.03 – – –
0.10 0.94 1.57 0.07 0.10 0.53 1.97 0.20 0.88 1.62 0.12 0.20 0.55 1.94 0.50 0.74 1.77 0.27 0.50 0.65 1.85 1.00 0.58 1.93 0.43 1.00 0.81 1.69 2.00 0.40 2.09 0.59 2.00 0.91 1.59 5.00 0.21 2.30 0.80 5.00 0.97 1.53 10.00 0.12 2.39 0.89 10.00 0.98 1.51 20.00 0.07 2.44 0.94 20.00 – – 50.00 0.03 2.48 0.98 50.00 – – 100.00 0.01 2.49 0.99 100.00 – – The equation for the random uncertainty Xc, in percent, in the value of the coefficient for all three flumes is:
Xc (1 + 20(Cv <CD) (7.22) The value of Cv and CD for all three flumes for the purpose of estimating the uncertainty Xc may be found from Tables I.7.6 and I.7.7, respectively.
These tables give approximate values and it should be emphasized if values of Cv and CD are required for calculating discharge the relevant standard
should be referred to, in this case ISO 4359 (1983).
7.9.6 Uncertainty in the measurement of the crest length or flume width, Xb
The length of crest or width of flume should be measured to within ± 0.10 per cent.
7.9.7 Random uncertainty in the head measurement, Xh
The random uncertainty Xh, in percent, may be found from the following equation:
X E E
h ( hh z
( )1/2=100 (7.23)
where Eh = uncertainty in the measurement of head by the recorder, in mm; EZ = uncertainty in the zeroing error in setting the recorder, in mm;
h = recorded head value, in mm.
References
Ackers, P., White, W.R., Perkins, J.A., and Harrison, A.J.M., 1978: Weirs and flumes for flow measurement.
John Wiley and Sons ISBN 0 471 99637 8.
Bos, M.G., 1976: Discharge measurement structures, Publication No. 161, Delft Hydraulics Laboratory, Delft.
Herschy, R.W., White, W.R. and Whitehead, E., 1977:
The design of Crump weirs. Technical Note No. 8.
Water Data Unit, Reading.
International Organization for Standardization, 1977:
Liquid flow measurement in open channels by weirs and flumes: End depth method for estimation of flow in rectangular channels with a free overfall. ISO 3847, Geneva.
International Organization for Standardization, 1983: Liquid flow measurement in open channels:
Rectangular, trapezoidal and U-shaped flumes.
ISO 4359, Geneva.
International Organization for Standardization, 1984:
Measurement of liquid flow in open channels by weirs and flumes: End depth method for estimation of flow in non-rectangular channels with a free overfall (approximate method). ISO 4371, Geneva.
International Organization for Standardization, 1985:
Liquid flow measurement in open channels by weirs and flumes: V-shaped broad-crested weirs. ISO 8333, Geneva.
International Organization for Standardization, 1990:
Liquid flow measurement in open channels: Round-nose horizontal broad-crested weirs. ISO 4374, Geneva.
[ ]
International Organization for Standardization, 1992:
Measurement of liquid flow in open channels: Parshall and SANIIRI flumes. ISO 9826, Geneva.
International Organization for Standardization, 1994:
Measurement of liquid flow in open channels by weirs and flumes: Streamlined triangular profile weirs.
ISO 9827, Geneva.
International Organization for Standardization, 1999:
Hydrometric determinations – Flow measurement in open channels using structures: Guidelines for selection of structure. ISO 8368, Geneva.
International Organization for Standardization, 1999:
Hydrometric determinations – Flow measurement in open channels using structures: Trapezoidal broad-crested weirs. ISO 4362, Geneva.
International Organization for Standardization, 2000:
Hydrometric determinations – Flow measurement in open channels using structures: Compound gauging structures. ISO 14139, Geneva.
International Organization for Standardization, 2002:
Hydrometric determinations – Flow measurement in open channels using structures: Flat-V weirs. ISO 4377, Geneva.
International Organization for Standardization, 2002:
Hydrometric determinations – Flow measurement in
open channels using structures: Use of vertical underflow gates. ISO 13550, Geneva.
International Organization for Standardization, 2005:
Water flow measurement in open channels using weirs and Venturi flumes; Part 1 – Thin plate weirs. ISO 1438-1, Geneva.
International Organization for Standardization, 2005:
Liquid flow measurement in open channels by weirs and flumes: Triangular profile weirs. ISO 4360, Geneva.
International Organization for Standardization, 2005:
Liquid flow measurement in open channels by weirs and flumes: Rectangular broad-crested weirs. ISO 3846, Geneva.
White, W.R., 1975: Field calibration of flow measuring structures: Proceedings Institution of Civil Engineers, Part 2, 59, pp. 429-447.
White, W.R., 1977: Thin-plate weirs, Proceedings. Institution of Civil Engineers, Part 2, 63, pp. 255-269. White, W.R., 1978: The use of measuring structures in stream gauging, in Hydrometry: Principles and Practices, John Wiley and Sons Ltd., London.
World Meteorological Organization, 1971: Use of Weirs and Flumes in Stream Gauging (WMO-No. 280), Technical Note No. 117, Geneva.